get.propagator: Propagator matrix G.

In spate: Spatio-Temporal Modeling of Large Data Using a Spectral SPDE Approach

Propagator matrix G.

Description

Function for obtaining the spectral propagator matrix G of the vector autoregressive model for the Fourier coefficients.

Usage

get.propagator(wave, indCos, zeta, rho1, gamma, alpha, muX, muY, dt = 1, ns=4)

Arguments

wave	Spatial wavenumbers.
indCos	Vector of integers indicating the position of columns in 'wave' of wavenumbers of cosine terms.
zeta	Damping parameter
rho1	Range parameter of the diffusion term
gamma	Parameter that determines the amount of anisotropy in the diffusion term
alpha	Parameter that determines the direction of anisotropy in the diffusion term
muX	X component of the drift vector.
muY	Y component of the drift vector.
dt	Temporal lag between two time points. By default, this equals 1.
ns	Number of real Fourier functions that have only a cosine and no sine term. 'ns' is maximal 4.

Value

Propagator matrix G.

Author(s)

Fabio Sigrist

Examples

##For illustration, four grid points on each axis
n <- 4
wave <- wave.numbers(n)
G <- get.propagator(wave=wave$wave,indCos=wave$indCos,zeta=0.5, rho1=0.1, gamma=2,
           alpha=pi/4, muX=0.2, muY=-0.15,dt=1,ns=4)
round(G,digits=2)
## View(round(G,digits=2))

##An example
n <- 50
spec <- matern.spec(wave=spate.init(n=n,T=1)$wave,n=n,rho0=0.05,sigma2=1,norm=TRUE)
alphat <- sqrt(spec)*rnorm(n*n)
##Propagate initial state
wave <- wave.numbers(n)
G <- get.propagator(wave=wave$wave,indCos=wave$indCos,zeta=0.5, rho1=0.02, gamma=2,
            alpha=pi/4, muX=0.2, muY=0.2,dt=1,ns=4)
alphat1 <- G%*%alphat

opar <- par(no.readonly = TRUE)
par(mfrow=c(1,2))
image(1:n,1:n,matrix(real.fft(alphat,n=n,inv=FALSE),nrow=n),main="Whittle
field",xlab="",ylab="",col=cols())
image(1:n,1:n,matrix(real.fft(alphat1,n=n,inv=FALSE),nrow=n),main="Propagated
field",xlab="",ylab="",col=cols())
par(opar) # Reset par() settings

spate documentation built on Oct. 3, 2023, 5:09 p.m.